Algebra 2 - Problem Set
Unit 1 Investigating Functions
Name:__________________
Block:_________
1) Consider the relation (4, 2),(4,3),(1,  4),(3, 2),(5,1)
a) State the domain and range of the relation.
D:___________________ R:_____________________
b) Create a mapping diagram and then a graph for the relation.
c) Is the relation a function? Why or why not?
______________________________________
2) State the domain and range for each of the following graphs. Then, state the intervals where the function is
increasing and where the function is decreasing.
a)
b)
D:___________
D:___________
R: ___________
R: ___________
Inc:__________
Inc:_________
Dec:_________
Dec:________
3) Using a calculator, graph each of the following. State the domain, range, and zeros of the function (if they
exist).
3
2
a) y   x  3  2
b) y   x  2   3
c) y  2  x  1  4
y
y
x
x
D:_________________
R:_________________
Algebra 2
Zeros:______________
y
D:_________________
R:_________________
Zeros:______________
x
D:_________________
R:_________________
Zeros:______________
d ) f ( x)  3 x  2  1
e) g ( x )  x  4  2
f ) h( x )  
y
y
2
x2 5
3
y
x
x
D:___________ R:___________
D:__________ R:___________
x
D:__________ R:___________
4) Select all of the following equations that have domain of all real numbers and a range of [-2,  )
1
f ( x)  x  3  2
2
a)
b) g ( x)  3x  2
c) y  2( x  3)2  2
d) h( x)  x  3  2
e) f ( x)  x3  2
f) g ( x)  3 x  4  2
5) Find the following using the following graph:
Domain:________________ Range:___________________
x-intercept(s):_________________ y-intercept:__________
Local minimum(s):_____________
Local maximum(s):_____________
Increasing interval(s):_______________________________
Decreasing interval(s):________________________________
6) Find the inverse of the following: { (2, 0), (0, -3), (5, 3), (5, -2)} _____________________________
State whether the inverse is a function or not:_____________________
Algebra 2
7) Using the graph below, determine if the graph is continuous. If not continuous, then determine the type of
discontinuities in the graph:
continuous?:______________________
If not, list the x-coordinate of the discontinuities:
_______________________________________
________________________________________
8) Describe the end behavior of the following functions:
a.
b.
As 𝑥 → −∞, 𝑓(𝑥) → ____________
As 𝑥 → −∞, 𝑓(𝑥) → ____________
As 𝑥 → ∞, 𝑓(𝑥) → ____________
As 𝑥 → ∞, 𝑓(𝑥) → ____________
9) Graph the inverse of the function:
Algebra 2
10) Is the curve an inverse of the coordinates?